Richardson worked with various Trotskyist groups, in particular Workers Liberty, Workers Action and the Militant tendency, whose approaches he felt were closest to his own. In contrast to these groups, he opposed any race, gender or sexuality based campaigns, which he believed were popular frontist. But he never abandoned the work inside Labour, because he believed that the revolutionary party can emerge only from a mass working-class party.

He continued teaching and writing until his death. Papers left by Richardson and Jim Higgins have been deposited in the Library of the University of London (located in the Senate House of the University).[2]